From b297de6d8e3b10b03cb33a45a145b2cf7c1f4509 Mon Sep 17 00:00:00 2001
From: todoit <zhaoyingguang@gmail.com>
Date: Mon, 9 May 2016 22:48:21 +0800
Subject: [PATCH 1/3] =?UTF-8?q?=E7=BA=BF=E6=80=A7=E4=BB=A3=E6=95=B0?=
 =?UTF-8?q?=E7=AC=94=E8=AE=B0?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 src/leetCode/__init__.py                      |   0
 src/leetCode/leetcode.py                      |  14 +
 .../homework1_circle.cpython-34.pyc           | Bin 1885 -> 2120 bytes
 src/todoit/MatPlot/circle_plot.py             |   2 +-
 src/todoit/MatPlot/homework_sort_fast.py      |  49 ++
 src/todoit/MatPlot/homework_sort_slow.py      |  49 ++
 src/todoit/linearAlgebra/__init__.py          |   0
 src/todoit/linearAlgebra/homework3-1.py       |  48 ++
 src/todoit/linearAlgebra/lesson22.py          |   8 +
 src/todoit/linearAlgebra/numpy_study_01.ipynb | 758 ++++++++++++++++++
 10 files changed, 927 insertions(+), 1 deletion(-)
 create mode 100644 src/leetCode/__init__.py
 create mode 100644 src/leetCode/leetcode.py
 create mode 100644 src/todoit/MatPlot/homework_sort_fast.py
 create mode 100644 src/todoit/MatPlot/homework_sort_slow.py
 create mode 100644 src/todoit/linearAlgebra/__init__.py
 create mode 100644 src/todoit/linearAlgebra/homework3-1.py
 create mode 100644 src/todoit/linearAlgebra/lesson22.py
 create mode 100644 src/todoit/linearAlgebra/numpy_study_01.ipynb

diff --git a/src/leetCode/__init__.py b/src/leetCode/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/src/leetCode/leetcode.py b/src/leetCode/leetcode.py
new file mode 100644
index 0000000..c8534fd
--- /dev/null
+++ b/src/leetCode/leetcode.py
@@ -0,0 +1,14 @@
+# -*- coding: utf-8 -*-
+
+'''
+Created on 2016年4月29日
+@author: todoit
+'''
+
+
+def reverseString(s):
+    return s[::-1]
+
+if __name__ == '__main__':
+    s = 'adsf asfd'
+    print(reverseString(s))
\ No newline at end of file
diff --git a/src/todoit/MatPlot/__pycache__/homework1_circle.cpython-34.pyc b/src/todoit/MatPlot/__pycache__/homework1_circle.cpython-34.pyc
index eee9d6456b54dbbfd017cf56934662678c59aa1e..50c0225a558199ee7a6bde05b42417ac11fe7d86 100644
GIT binary patch
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diff --git a/src/todoit/MatPlot/circle_plot.py b/src/todoit/MatPlot/circle_plot.py
index a9d0b98..e005609 100644
--- a/src/todoit/MatPlot/circle_plot.py
+++ b/src/todoit/MatPlot/circle_plot.py
@@ -6,7 +6,7 @@
 
 from todoit.MatPlot.homework1_circle import gen_circle_point
 
-N=16
+N=64
 
 fig = plt.figure()
 
diff --git a/src/todoit/MatPlot/homework_sort_fast.py b/src/todoit/MatPlot/homework_sort_fast.py
new file mode 100644
index 0000000..b812fee
--- /dev/null
+++ b/src/todoit/MatPlot/homework_sort_fast.py
@@ -0,0 +1,49 @@
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+# CopyRight by heibanke
+
+import matplotlib.pyplot as plt
+import numpy as np
+import matplotlib.animation as animation
+
+def f(t):
+    s1 = np.sin(2 * np.pi * t)
+    e1 = np.exp(-t)
+    return np.absolute((s1 * e1)) + .05
+    
+
+def bubbleSort():
+    nums = s
+    for j in xrange(len(nums),-1,-1):
+        for i in xrange(0,j-1,1):
+            if nums[i] > nums[i+1]:
+                nums[i],nums[i+1] = nums[i+1],nums[i]
+                
+        yield nums
+    
+def update(data):  
+    for i in xrange(len(lines)):
+        lines[i].set_ydata([0,data[i]])  
+    return lines
+
+    
+t = np.arange(0.0, 5.0, 0.1)
+s = f(t) 
+    
+fig = plt.figure(figsize=(12, 6))
+ax = fig.add_subplot(111)
+
+lines=[]
+
+for i in xrange(len(t)):
+    line,=ax.plot([i,i], [0,s[i]] , 'b-o')
+    lines.append(line)
+
+ax.set_xlabel('index')
+ax.set_ylabel('value')
+ax.set_title('BubbleSort')
+
+    
+ani = animation.FuncAnimation(fig, update, bubbleSort, interval=10, repeat=False)  
+
+plt.show()
\ No newline at end of file
diff --git a/src/todoit/MatPlot/homework_sort_slow.py b/src/todoit/MatPlot/homework_sort_slow.py
new file mode 100644
index 0000000..86ced72
--- /dev/null
+++ b/src/todoit/MatPlot/homework_sort_slow.py
@@ -0,0 +1,49 @@
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+# CopyRight by heibanke
+
+import matplotlib.pyplot as plt
+import numpy as np
+import matplotlib.animation as animation
+
+def f(t):
+    s1 = np.sin(2 * np.pi * t)
+    e1 = np.exp(-t)
+    return np.absolute((s1 * e1)) + .05
+    
+
+def bubbleSort():
+    nums = s
+    for j in xrange(len(nums),-1,-1):
+        for i in xrange(0,j-1,1):
+            if nums[i] > nums[i+1]:
+                nums[i],nums[i+1] = nums[i+1],nums[i]
+                
+            yield nums
+    
+def update(data):  
+    for i in xrange(len(lines)):
+        lines[i].set_ydata([0,data[i]])  
+    return lines
+
+    
+t = np.arange(0.0, 5.0, 0.1)
+s = f(t) 
+    
+fig = plt.figure(figsize=(12, 6))
+ax = fig.add_subplot(111)
+
+lines=[]
+
+for i in xrange(len(t)):
+    line,=ax.plot([i,i], [0,s[i]] , 'b-o')
+    lines.append(line)
+
+ax.set_xlabel('index')
+ax.set_ylabel('value')
+ax.set_title('BubbleSort')
+
+    
+ani = animation.FuncAnimation(fig, update, bubbleSort, interval=10, repeat=False)  
+
+plt.show()
\ No newline at end of file
diff --git a/src/todoit/linearAlgebra/__init__.py b/src/todoit/linearAlgebra/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/src/todoit/linearAlgebra/homework3-1.py b/src/todoit/linearAlgebra/homework3-1.py
new file mode 100644
index 0000000..59d0100
--- /dev/null
+++ b/src/todoit/linearAlgebra/homework3-1.py
@@ -0,0 +1,48 @@
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+#copyRight by heibanke 
+#%matplotlib inline
+
+from matplotlib import pyplot as plt
+import numpy as np
+
+A=np.array([[3],[1]])
+C=np.array([[1],[3]])
+
+x=np.linspace(-2,2,10)
+
+"""
+x相当于是一维的点。
+xx＝Ax相当于讲解图中的OA这条直线。为了打直线图引入的变量。
+3x是这条直线的横坐标范围，x是这条直线的纵坐标范围
+这里也可以不引入这么多点，引入两个点就行，不过这样可以和后续代码保持一致。
+"""
+x.shape=(1,10)
+xx=A.dot(x)
+
+
+B=A.T.dot(C)
+AA=np.linalg.inv(A.T.dot(A))
+
+#P=Ax^=A*AA*B
+P=A*AA*B
+E=C-P
+
+fig = plt.figure() #figsize=(10,6)
+ax= fig.add_subplot(111)
+
+ax.plot(xx[0,:],xx[1,:])
+ax.plot(A[0],A[1],'ko')
+ax.plot([C[0],P[0]],[C[1],P[1]],'r-o')
+ax.plot([0,C[0]],[0,C[1]],'m-o')
+ax.plot([0,E[0]],[0,E[1]],'k-o')
+
+margin=0.1
+ax.text(A[0]+margin, A[1]+margin, r"A",fontsize=20)
+ax.text(C[0]+margin, C[1]+margin, r"C",fontsize=20)
+ax.text(P[0]+margin, P[1]+margin, r"P",fontsize=20)
+ax.text(E[0]+margin, E[1]+margin, r"E",fontsize=20)
+
+
+ax.axis('equal')
+plt.show()
\ No newline at end of file
diff --git a/src/todoit/linearAlgebra/lesson22.py b/src/todoit/linearAlgebra/lesson22.py
new file mode 100644
index 0000000..997cdbc
--- /dev/null
+++ b/src/todoit/linearAlgebra/lesson22.py
@@ -0,0 +1,8 @@
+# -*- coding: utf-8 -*-
+
+'''
+Created on 2016年5月9日
+@author: todoit
+'''
+
+
diff --git a/src/todoit/linearAlgebra/numpy_study_01.ipynb b/src/todoit/linearAlgebra/numpy_study_01.ipynb
new file mode 100644
index 0000000..b4d5280
--- /dev/null
+++ b/src/todoit/linearAlgebra/numpy_study_01.ipynb
@@ -0,0 +1,758 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# numpy基础入门 ——by 黑板客"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 1. 矩阵的创建"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[1 2 3 4] [1 2 3 4 5] int32 (4,) 4 1\n"
+     ]
+    }
+   ],
+   "source": [
+    "a=np.arange(1,5)\n",
+    "b=np.array([1,2,3,4,5])\n",
+    "print(a, b, a.dtype, a.shape, a.size, a.ndim)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "    np.arange类似range函数\n",
+    "    np.array用来生成矩阵\n",
+    "    dtype是数据类型，有int64, complex, uint16等\n",
+    "    shape是个元组属性，表示每一维的宽度\n",
+    "    size是所有元素个数\n",
+    "    ndim是维数"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[1 2 3] int64\n"
+     ]
+    }
+   ],
+   "source": [
+    "b=np.array([1,2,3],dtype='int64') # int64, complex, uint16......\n",
+    "print(b, b.dtype)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0 1 2 3 4 5]\n",
+      " [0 1 2 3 4 5]\n",
+      " [0 1 2 3 4 5]] (3, 6) 18\n"
+     ]
+    }
+   ],
+   "source": [
+    "m=np.array([np.arange(6),np.arange(6),np.arange(6)])\n",
+    "print(m, m.shape, m.size)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[1 2 3 4]\n",
+      " [5 6 7 8]] 3 6\n",
+      "3 6\n",
+      "[[[ 1  2  3]\n",
+      "  [ 4  5  6]]\n",
+      "\n",
+      " [[ 7  8  9]\n",
+      "  [10 11 12]]] (2, 2, 3)\n",
+      "[7 8 9]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "numpy.ndarray"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# 每一个[]代表一维，比如\n",
+    "# [[[1,2,3],[4,5,6]],[[7,8,9],[10,11,12]]], 代表矩阵的维度是(2,2,3)\n",
+    "# 其中第一个2，代表最外层的两个[]，第二个2代表第二层[]，第三个3代表最里层的维度。\n",
+    "n=np.array([[1,2,3,4],[5,6,7,8]])\n",
+    "\n",
+    "#下面这两种用法一样吗？？\n",
+    "print(n, n[0,2], n[1,1])\n",
+    "print(n[0][2], n[1][1])\n",
+    "\n",
+    "m=np.array([[[1,2,3],[4,5,6]],[[7,8,9],[10,11,12]]])\n",
+    "print(m, m.shape)\n",
+    "print(m[1,0])\n",
+    "type(m)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[[ 1  2  3]\n",
+      "  [ 4  5  6]]\n",
+      "\n",
+      " [[ 7  8  9]\n",
+      "  [10 11 12]]]\n",
+      "[[1 2 3 4]\n",
+      " [5 6 7 8]]\n",
+      "[ 1  2  3  4  5  6  7  8  9 10 11 12]\n",
+      "[1 2 3 4 5 6 7 8]\n"
+     ]
+    }
+   ],
+   "source": [
+    "x=m.ravel()\n",
+    "y=n.flatten()\n",
+    "print(m)\n",
+    "print(n)\n",
+    "print(x)\n",
+    "\n",
+    "print(y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "    ravel()和flatten()看起来效果一样，都是把矩阵展平了。它们的区别在于\n",
+    "    ravel()返回的是原有数据的一个映射(view)，没有分配新的存储\n",
+    "    flatten()返回的是新的数据\n",
+    "    因此如果我们改变它们的值，就可以看出区别\n",
+    "    \n",
+    "    numpy还有一些函数有这样的区别，关键在于判断函数返回是原数据的映射还是返回新的数据。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[[ 1  2  3]\n",
+      "  [10  5  6]]\n",
+      "\n",
+      " [[ 7  8  9]\n",
+      "  [10 11 12]]]\n",
+      "[[1 2 3 4]\n",
+      " [5 6 7 8]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "x[3]=10;y[3]=10\n",
+    "print(m)\n",
+    "print(n)\n",
+    "# 看看m，n哪个的值改变了"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## reshap 和 resize"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 1  2  3 10]\n",
+      " [ 5  6  7  8]\n",
+      " [ 9 10 11 12]] None \n",
+      " [[1 2 3 4]\n",
+      " [5 6 7 8]\n",
+      " [0 0 0 0]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# reshape返回一个view\n",
+    "x=m.reshape(3,4)\n",
+    "# resize直接在当前数据上更改，返回空\n",
+    "y=n.resize(3,4)\n",
+    "print(x,y,'\\n',n)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 1  2  3 10]\n",
+      " [ 5  6  7  8]\n",
+      " [10 10 10 10]]\n",
+      "[[[ 1  2  3]\n",
+      "  [10  5  6]]\n",
+      "\n",
+      " [[ 7  8 10]\n",
+      "  [10 10 10]]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "x[2]=10\n",
+    "print(x)\n",
+    "print(m)\n",
+    "# 看看m和n哪个改变了，有什么区别"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 0  1  2  3]\n",
+      " [ 4  5  0  1]\n",
+      " [10 10 10 10]]\n",
+      "[[0 1 2 3 4 5]\n",
+      " [0 1 2 3 4 5]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "m=np.array([np.arange(6),np.arange(6)])\n",
+    "# copy()可以强制返回一个新的数据\n",
+    "x=m.reshape(3,4).copy()\n",
+    "x[2]=10;print(x);print(m)\n",
+    "#看看这次m的值随x改变而改变吗"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[ 0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1. ]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# linspace返回0,1之间的10个数据，它们之间的间隔自动计算\n",
+    "x=np.linspace(0.1,1,10)\n",
+    "print(x)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0 3 5 7 6 9 1 2 8 4]\n",
+      "[[0 1 2]\n",
+      " [3 4 5]\n",
+      " [6 7 8]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "a = np.arange(10)\n",
+    "np.random.shuffle(a)  # 随机排第一维\n",
+    "print(a)\n",
+    "\n",
+    "a = np.arange(9).reshape((3, 3)) # 随机排第一维，想一想结果是什么\n",
+    "np.random.shuffle(a)\n",
+    "print(a)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 1.,  1.,  1.,  1.])"
+      ]
+     },
+     "execution_count": 48,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# 全0矩阵\n",
+    "a=np.zeros((3,3))\n",
+    "# 全1矩阵\n",
+    "b=np.ones((5,4))\n",
+    "# 单位矩阵\n",
+    "c=np.eye(3)\n",
+    "# 取对角元素\n",
+    "np.diag(b)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 2. 矩阵的加法"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0 1 2]\n",
+      " [3 4 5]\n",
+      " [6 7 8]]\n",
+      "[[ 3  4  5]\n",
+      " [ 6  7  8]\n",
+      " [ 9 10 11]]\n",
+      "[[ 0  2  4]\n",
+      " [ 3  5  7]\n",
+      " [ 6  8 10]]\n",
+      "[[ 0  1  2]\n",
+      " [ 4  5  6]\n",
+      " [ 8  9 10]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "a = np.arange(9).reshape((3, 3))\n",
+    "\n",
+    "## 每个元素的broadcast\n",
+    "print(a)\n",
+    "print(a+3)\n",
+    "\n",
+    "## 行broadcast\n",
+    "print(a+np.arange(3))\n",
+    "\n",
+    "## 列broadcast\n",
+    "print(a+np.arange(3).reshape(3,1))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## broadcast广播操作\n",
+    "    运算不仅仅作用在某个元素，而是作用在整个矩阵，或者整行，或者整列。\n",
+    "    比如\n",
+    "    n*m + 1*1 就是将1*1的元素作用在n*m的整个矩阵\n",
+    "    n*m + n*1 就是将n*1的元素作用在n*m的每一列\n",
+    "    n*m + 1*m 就是将1*m的元素作用在n*m的每一行\n",
+    "    乘法类似"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[4 6]\n",
+      "[3 7]\n",
+      "[ 2.  3.]\n",
+      "[ 1.5  3.5]\n",
+      "[ 1.  1.]\n",
+      "[[ 6  8 10]\n",
+      " [12 14 16]]\n",
+      "[[ 3  5  7]\n",
+      " [15 17 19]]\n",
+      "[[ 3 12]\n",
+      " [21 30]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "a = np.array([[1, 2], [3, 4]])\n",
+    "print(np.sum(a,axis=0))\n",
+    "print(np.sum(a,axis=1))\n",
+    "print(np.mean(a,axis=0))\n",
+    "print(np.mean(a,axis=1))\n",
+    "print(np.std(a,axis=0))\n",
+    "\n",
+    "#axis=0，就是按第一个维度进行计算，行向量[1,2], [3,4]\n",
+    "#axis=1，就是按第二个维度进行计算，列向量[1,3], [2,4]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 6  8 10]\n",
+      " [12 14 16]]\n",
+      "[[ 3  5  7]\n",
+      " [15 17 19]]\n",
+      "[[ 3 12]\n",
+      " [21 30]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "#再拓展到3维\n",
+    "a = np.arange(12).reshape((2,2,3))\n",
+    "print np.sum(a,axis=0) #按第一维度加，结果为2*3矩阵, 可以理解为1*2*3\n",
+    "print np.sum(a,axis=1) #按第二维度加，结果为2*3矩阵, 可以理解为2*1*3\n",
+    "print np.sum(a,axis=2) #按第三维度加，结果为2*2矩阵, 可以理解为2*2*1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 3. 矩阵的转置"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0 0]\n",
+      " [1 1]\n",
+      " [2 2]\n",
+      " [3 3]\n",
+      " [4 4]\n",
+      " [5 5]]\n",
+      "[[0 0]\n",
+      " [1 1]\n",
+      " [2 2]\n",
+      " [3 3]\n",
+      " [4 4]\n",
+      " [5 5]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(m.transpose())\n",
+    "print(m.T)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 4. 矩阵的乘法"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "a = np.arange(12).reshape((6, 2))\n",
+    "b = np.arange(10).reshape((2,5))\n",
+    "\n",
+    "# 两种矩阵乘法形式\n",
+    "print a.dot(b)\n",
+    "print np.dot(a,b)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "## 每个元素broadcast\n",
+    "print a*2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# 行broadcast\n",
+    "print a*[1,2]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# 列broadcast\n",
+    "print a*np.arange(6).reshape(6,1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 5.矩阵的拼接"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "a = np.arange(9).reshape(3,3)\n",
+    "b = 2 * a\n",
+    "c = np.hstack((a, b))\n",
+    "print c"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "print np.concatenate((a, b), axis=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "c=np.vstack((a, b))\n",
+    "c=np.concatenate((a, b), axis=0)\n",
+    "\n",
+    "print np.hsplit(a, 3)\n",
+    "print np.vsplit(a,3)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 6. 矩阵的查找"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "a = np.arange(12).reshape((3, 4))\n",
+    "b = a%2==0\n",
+    "c = a>4\n",
+    "print b\n",
+    "print c\n",
+    "# 这里也用到了broadcast"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "a = np.arange(12).reshape((3, 4))\n",
+    "print a\n",
+    "print np.argmax(a)\n",
+    "# 其实是列broadcast，返回每列最大值的idx\n",
+    "print np.argmax(a, axis=0)\n",
+    "\n",
+    "# 行broadcast，返回每行最大值的idx\n",
+    "print np.argmax(a, axis=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# np.where支持多个逻辑组合, 得到满足条件的index\n",
+    "idx=np.where((a>3))\n",
+    "print a[idx]\n",
+    "\n",
+    "idx=np.where((a>3)&(a<7))\n",
+    "print a[idx]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 7. homework"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "1. http://www.labri.fr/perso/nrougier/teaching/numpy.100/"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.4.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}

From b542898ff8c93c6894d15e3650353d9d258258da Mon Sep 17 00:00:00 2001
From: todoit <zhaoyingguang@gmail.com>
Date: Sun, 15 May 2016 23:55:42 +0800
Subject: [PATCH 2/3] =?UTF-8?q?=E6=9C=80=E5=B0=8F=E4=BA=8C=E4=B9=98?=
 =?UTF-8?q?=E5=AD=A6=E4=B9=A0?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 src/todoit/MatPlot/homework_3_v2.py           |  4 +-
 src/todoit/linearAlgebra/homework3-1.py       |  3 ++
 src/todoit/linearAlgebra/homework_zuixiao1.py | 32 +++++++++++++++
 src/todoit/linearAlgebra/zuixiao1.py          | 40 +++++++++++++++++++
 4 files changed, 77 insertions(+), 2 deletions(-)
 create mode 100644 src/todoit/linearAlgebra/homework_zuixiao1.py
 create mode 100644 src/todoit/linearAlgebra/zuixiao1.py

diff --git a/src/todoit/MatPlot/homework_3_v2.py b/src/todoit/MatPlot/homework_3_v2.py
index 65e2300..6500654 100644
--- a/src/todoit/MatPlot/homework_3_v2.py
+++ b/src/todoit/MatPlot/homework_3_v2.py
@@ -139,12 +139,12 @@ def updateAll(i):
     #这里的frames至少应该为data的长度
     anims = animation.FuncAnimation(fig, updateAll,init_func=init, blit=False, frames=len(data), interval=500, repeat=True)
     
-    #plt.show()
+    plt.show()
 
     # FFwriter = animation.FFMpegWriter()
     # Set up formatting for the movie files fps = frames per second
     #anims.save('D:/MovWave.mp4', writer=FFwriter, fps=1,dpi=300)
     
-    anims.save('D:/homework_3.gif', fps=2, writer='imagemagick')
+    #anims.save('D:/homework_3.gif', fps=2, writer='imagemagick')
     
     
diff --git a/src/todoit/linearAlgebra/homework3-1.py b/src/todoit/linearAlgebra/homework3-1.py
index 59d0100..a86d170 100644
--- a/src/todoit/linearAlgebra/homework3-1.py
+++ b/src/todoit/linearAlgebra/homework3-1.py
@@ -7,6 +7,7 @@
 import numpy as np
 
 A=np.array([[3],[1]])
+
 C=np.array([[1],[3]])
 
 x=np.linspace(-2,2,10)
@@ -25,7 +26,9 @@
 AA=np.linalg.inv(A.T.dot(A))
 
 #P=Ax^=A*AA*B
+#得到投影后的向量
 P=A*AA*B
+#投影在另一个维度上的向量
 E=C-P
 
 fig = plt.figure() #figsize=(10,6)
diff --git a/src/todoit/linearAlgebra/homework_zuixiao1.py b/src/todoit/linearAlgebra/homework_zuixiao1.py
new file mode 100644
index 0000000..aa64676
--- /dev/null
+++ b/src/todoit/linearAlgebra/homework_zuixiao1.py
@@ -0,0 +1,32 @@
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+#copyRight by heibanke 
+
+import numpy as np  
+import matplotlib.pyplot as plt  
+    
+x = np.linspace(-1,1,100)  
+y = 2*np.sin(x*2.3)+0.5*x**3
+
+y1 = y+0.5*(np.random.rand(len(x))-0.5)
+
+A = np.vstack((x,np.ones(len(x)))).T
+b = y1.reshape(y1.shape[0],1)
+
+def projection(A,b):
+    ####
+    # return A*inv(AT*A)*AT*b
+    ####
+    AA = A.T.dot(A)
+    w=np.linalg.inv(AA).dot(A.T).dot(b)
+    print w
+    return A.dot(w)
+
+yw = projection(A,b)
+yw.shape = (yw.shape[0],)
+
+plt.plot(x,y,color='g',linestyle='-',marker='') 
+plt.plot(x,y1,color='m',linestyle='',marker='o')
+plt.plot(x,yw,color='r',linestyle='',marker='.')
+
+plt.show()
diff --git a/src/todoit/linearAlgebra/zuixiao1.py b/src/todoit/linearAlgebra/zuixiao1.py
new file mode 100644
index 0000000..3f66e4b
--- /dev/null
+++ b/src/todoit/linearAlgebra/zuixiao1.py
@@ -0,0 +1,40 @@
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+#copyRight by heibanke 
+
+import numpy as np  
+import matplotlib.pyplot as plt  
+    
+x = np.linspace(-1,1,100)  
+y = 2*np.sin(x*2.3)+0.5*x**3
+
+y1 = y+0.5*(np.random.rand(len(x))-0.5)
+
+c = np.tile([1],100)
+
+##################################
+# 写下你的Code
+#Ax^=b,求出x^,即可得到直线y=ax+b
+#向量A是一个100维的向量，第一列是x1...x100,第二列是1
+A = np.array([x,c]).T
+#A = np.vstack((x,np.ones(len(x)))).T
+#b是y1...y100
+b = np.array([y1]).T
+#b = y1.reshape(y1.shape[0],1)
+#根据公式求x^
+x_bar = (np.linalg.inv(A.T.dot(A))).dot(A.T).dot(b)
+
+#计算直线
+
+y2 = A.dot(x_bar)
+
+y2.shape = (y2.shape[0],)
+##################################
+plt.plot(x,y,color='g',linestyle='-',marker='') 
+plt.plot(x,y1,color='m',linestyle='',marker='o')
+
+plt.plot(x,y2,color='b',linestyle='-',marker='')
+
+# 把拟合的曲线在这里画出来
+
+plt.show()

From 67a511b2ed1cbba1d8f5f63fc4c466d68c1b079d Mon Sep 17 00:00:00 2001
From: todoit <zhaoyingguang@gmail.com>
Date: Sat, 11 Jun 2016 23:03:18 +0800
Subject: [PATCH 3/3] =?UTF-8?q?'=E8=AF=BE=E6=97=B633=E4=BD=9C=E4=B8=9A'?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .../__pycache__/load_MNIST.cpython-34.pyc     | Bin 0 -> 2779 bytes
 .../__pycache__/solutions_3.cpython-34.pyc    | Bin 0 -> 1617 bytes
 src/todoit/linearAlgebra/homework_zuixiao1.py |   2 +-
 src/todoit/linearAlgebra/homework_zuixiao2.py |  41 +++++++
 src/todoit/linearAlgebra/hw_3-1.py            |  38 ++++++
 src/todoit/linearAlgebra/hw_3-2.py            |  27 +++++
 src/todoit/linearAlgebra/hw_3-3.py            |  14 +++
 src/todoit/linearAlgebra/hw_3-4.py            |  72 +++++++++++
 src/todoit/linearAlgebra/hw_3-5.py            |  29 +++++
 src/todoit/linearAlgebra/hw_3-6_pca.py        |  28 +++++
 src/todoit/linearAlgebra/leastsqTest.py       |  45 +++++++
 src/todoit/linearAlgebra/load_MNIST.py        | 113 ++++++++++++++++++
 src/todoit/linearAlgebra/pca01.py             |  43 +++++++
 src/todoit/linearAlgebra/solutions_3.py       |  69 +++++++++++
 src/todoit/linearAlgebra/svd_demo.py          |  33 +++++
 src/todoit/linearAlgebra/test.py              |   8 ++
 src/todoit/linearAlgebra/zuixiao2.py          |  46 +++++++
 17 files changed, 607 insertions(+), 1 deletion(-)
 create mode 100644 src/todoit/linearAlgebra/__pycache__/load_MNIST.cpython-34.pyc
 create mode 100644 src/todoit/linearAlgebra/__pycache__/solutions_3.cpython-34.pyc
 create mode 100644 src/todoit/linearAlgebra/homework_zuixiao2.py
 create mode 100644 src/todoit/linearAlgebra/hw_3-1.py
 create mode 100644 src/todoit/linearAlgebra/hw_3-2.py
 create mode 100644 src/todoit/linearAlgebra/hw_3-3.py
 create mode 100644 src/todoit/linearAlgebra/hw_3-4.py
 create mode 100644 src/todoit/linearAlgebra/hw_3-5.py
 create mode 100644 src/todoit/linearAlgebra/hw_3-6_pca.py
 create mode 100644 src/todoit/linearAlgebra/leastsqTest.py
 create mode 100644 src/todoit/linearAlgebra/load_MNIST.py
 create mode 100644 src/todoit/linearAlgebra/pca01.py
 create mode 100644 src/todoit/linearAlgebra/solutions_3.py
 create mode 100644 src/todoit/linearAlgebra/svd_demo.py
 create mode 100644 src/todoit/linearAlgebra/test.py
 create mode 100644 src/todoit/linearAlgebra/zuixiao2.py

diff --git a/src/todoit/linearAlgebra/__pycache__/load_MNIST.cpython-34.pyc b/src/todoit/linearAlgebra/__pycache__/load_MNIST.cpython-34.pyc
new file mode 100644
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diff --git a/src/todoit/linearAlgebra/homework_zuixiao1.py b/src/todoit/linearAlgebra/homework_zuixiao1.py
index aa64676..2746a61 100644
--- a/src/todoit/linearAlgebra/homework_zuixiao1.py
+++ b/src/todoit/linearAlgebra/homework_zuixiao1.py
@@ -19,7 +19,7 @@ def projection(A,b):
     ####
     AA = A.T.dot(A)
     w=np.linalg.inv(AA).dot(A.T).dot(b)
-    print w
+    print(w)
     return A.dot(w)
 
 yw = projection(A,b)
diff --git a/src/todoit/linearAlgebra/homework_zuixiao2.py b/src/todoit/linearAlgebra/homework_zuixiao2.py
new file mode 100644
index 0000000..e769b16
--- /dev/null
+++ b/src/todoit/linearAlgebra/homework_zuixiao2.py
@@ -0,0 +1,41 @@
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+#copyRight by heibanke 
+
+import numpy as np  
+import matplotlib.pyplot as plt  
+    
+x = np.linspace(-1,1,100)  
+y = ((x*x-1)**3+1)*(np.cos(x*2)+0.6*np.sin(x*1.3))
+
+y1 = y+(np.random.rand(len(x))-0.5)
+
+m = []
+for i in range(7):
+    print(i)
+    m.append(x**(i))
+    print(m)
+
+
+A = np.array(m).T
+b = y1.reshape(y1.shape[0],1)
+
+#投影函数
+def projection(A,b):
+    ####
+    # return A*inv(AT*A)*AT*b
+    ####
+    AA = A.T.dot(A)
+    w=np.linalg.inv(AA).dot(A.T).dot(b)
+    print(w)
+    return A.dot(w)
+
+yw = projection(A,b)
+yw.shape = (yw.shape[0],)
+
+plt.plot(x,y,color='g',linestyle='-',marker='',label=u"理想曲线") 
+plt.plot(x,y1,color='m',linestyle='',marker='o',label=u"已知数据点")
+plt.plot(x,yw,color='r',linestyle='-',marker='.',label=u"拟合曲线")
+
+plt.legend()
+plt.show()
diff --git a/src/todoit/linearAlgebra/hw_3-1.py b/src/todoit/linearAlgebra/hw_3-1.py
new file mode 100644
index 0000000..8eb6bb7
--- /dev/null
+++ b/src/todoit/linearAlgebra/hw_3-1.py
@@ -0,0 +1,38 @@
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+#copyRight by heibanke 
+
+# Gram-Schmidt
+
+from matplotlib import pyplot as plt
+import numpy as np
+from mpl_toolkits.mplot3d import Axes3D
+
+
+A=np.array([[1],[2],[3]])
+B=np.array([[1],[1],[1]])
+
+x=np.linspace(-0.5,1,10)
+
+x.shape=(1,10)
+xx=A.dot(x)
+
+C=A.T.dot(B)
+AA=np.linalg.inv(A.T.dot(A))
+
+P=A.dot(AA).dot(C)
+E=B-P
+
+
+fig = plt.figure() 
+ax = fig.gca(projection='3d')
+
+ax.plot(xx[0,:],xx[1,:],xx[2,:],label="lineA")
+ax.plot(A[0],A[1],A[2],'ko',label="A")
+ax.plot([0,B[0]],[0,B[1]],[0,B[2]],'m-o',label="0B")
+ax.plot([B[0][0],P[0][0]],[B[1][0],P[1][0]],[B[2][0],P[2][0]],'r-o',label="BP")
+ax.plot([0,E[0]],[0,E[1]],[0,E[2]],'y-o',label="0E")
+
+ax.legend()
+ax.axis('equal')
+plt.show()
diff --git a/src/todoit/linearAlgebra/hw_3-2.py b/src/todoit/linearAlgebra/hw_3-2.py
new file mode 100644
index 0000000..d757698
--- /dev/null
+++ b/src/todoit/linearAlgebra/hw_3-2.py
@@ -0,0 +1,27 @@
+#!/usr/bin/env python
+# coding: utf-8
+#copyRight by heibanke
+
+import numpy as np  
+import matplotlib.pyplot as plt  
+from solutions_3 import *
+
+# 产生一个方波(x,y)
+x = np.linspace(-10,10,300) 
+y=[]
+for i in np.cos(x):
+    if i>0:
+        y.append(0)
+    else:
+        y.append(2)
+y=np.array(y)
+
+# write Your code, Fourier function    
+plt.plot(x,y,color='g',label='origin') 
+plt.plot(x,fourier(x,y,3),color='r',label='3')
+plt.plot(x,fourier(x,y,8),color='b',label='8')
+plt.plot(x,fourier(x,y,23),color='k',label='23')
+
+plt.legend()
+plt.axis('equal')
+plt.show()
diff --git a/src/todoit/linearAlgebra/hw_3-3.py b/src/todoit/linearAlgebra/hw_3-3.py
new file mode 100644
index 0000000..8f2d885
--- /dev/null
+++ b/src/todoit/linearAlgebra/hw_3-3.py
@@ -0,0 +1,14 @@
+#!/usr/bin/env python
+# coding: utf-8
+#copyRight by heibanke
+
+import numpy as np  
+import matplotlib.pyplot as plt  
+from solutions_3 import *
+
+A=np.array([[3,1],[2,4]])/4.0
+
+# write Your code
+# def eigshow(A):
+
+eigshow(A)
\ No newline at end of file
diff --git a/src/todoit/linearAlgebra/hw_3-4.py b/src/todoit/linearAlgebra/hw_3-4.py
new file mode 100644
index 0000000..46b3380
--- /dev/null
+++ b/src/todoit/linearAlgebra/hw_3-4.py
@@ -0,0 +1,72 @@
+#!/usr/bin/env python
+# coding: utf-8
+#copyRight by heibanke
+
+import numpy as np  
+
+import time
+def time_cost(f):
+    def _f(*arg, **kwarg):
+        start = time.clock()
+        a=f(*arg,**kwarg)
+        end = time.clock()
+        print(f.__name__,"run cost time is ",end-start)
+        return a
+    return _f
+
+   
+@time_cost
+def fib_opt_seq(seq):
+    return [fib_opt(i) for i in seq]
+    
+def fib_opt(n):
+    a,b,i=0,1,0
+    
+    while i<n:
+        a,b=b,a+b
+        i+=1
+    else:
+        return b    
+
+
+
+#使用特征根方法求斐波那契数列
+#因为只需要计算一次，写在函数外部
+A = np.array([[1,1],[1,0]]);
+u_0 = np.array([[1,0],]).T
+#求A的特征值和特征向量 
+eigVals, eigVects = np.linalg.eig(A) 
+
+#计算S和S的逆
+S = eigVects
+S_inv = np.linalg.inv(S) 
+#计算lambda  的值
+L = np.diag(eigVals) #生成对角矩阵
+
+def fib_eig(n):
+    #计算uk，n如果过大（2000）会造成溢出，
+    u_k = S.dot(L**n).dot(S_inv).dot(u_0)
+    #返回第一个元素
+    return u_k[0,0]
+
+@time_cost
+def fib_eig_seq(n):   
+    return [fib_eig(i) for i in seq] 
+
+        
+import random
+#seq = [random.randint(800,1000) for i in xrange(1000)]
+seq = range(1000)
+a=fib_opt_seq(seq)
+#print(a)
+print(a[-1])
+
+# write Your code fib_eig_seq function
+# 特征根方法计算效率明显比递归方法高，但是结果中会有小数，并非完全精确
+b=fib_eig_seq(seq)
+#print(b)
+print(b[-1])
+
+
+
+
diff --git a/src/todoit/linearAlgebra/hw_3-5.py b/src/todoit/linearAlgebra/hw_3-5.py
new file mode 100644
index 0000000..6c55cf1
--- /dev/null
+++ b/src/todoit/linearAlgebra/hw_3-5.py
@@ -0,0 +1,29 @@
+# coding: utf-8
+
+import numpy as np  
+
+#时间
+years = 100
+
+#差分方程变为矩阵乘法
+A = np.array([[0.8,0.1],[0.2,0.9]]);
+
+#初始化的人数
+population_init = np.array([[3200,4000],]).T 
+
+#求A的特征值和特征向量 
+eigVals, eigVects = np.linalg.eig(A) 
+
+#计算S和S的逆
+S = eigVects
+S_inv = np.linalg.inv(S) 
+#计算lambda 的值
+L = np.diag(eigVals) #由特征向量生成对角矩阵
+
+population_num = S.dot(L**years).dot(S_inv).dot(population_init)
+
+print(population_num)
+
+
+
+
diff --git a/src/todoit/linearAlgebra/hw_3-6_pca.py b/src/todoit/linearAlgebra/hw_3-6_pca.py
new file mode 100644
index 0000000..39f2d11
--- /dev/null
+++ b/src/todoit/linearAlgebra/hw_3-6_pca.py
@@ -0,0 +1,28 @@
+#!/usr/bin/env python
+# coding: utf-8
+#copyRight by heibanke
+
+import numpy as np
+import matplotlib.pyplot as plt  
+from load_MNIST import *
+from solutions_3 import *
+
+
+trainX,trainy,testX,testy=get_data(Only0=False,N=2000)
+data=trainX[:,1:]
+
+"""
+# write Your code
+# def pca(data,k=0.9):
+    # data 原始的图片
+    # k是保留特征值的百分比
+    # return 返回降维后重建的图片
+
+# def show_pic(origin_data, low_dim_):
+
+# N is number of pic to show in the figure
+"""
+N = 20
+recon_data = pca(data,k=0.9)
+show_pic(data[:N,:],recon_data[:N,:])
+
diff --git a/src/todoit/linearAlgebra/leastsqTest.py b/src/todoit/linearAlgebra/leastsqTest.py
new file mode 100644
index 0000000..8e7f52c
--- /dev/null
+++ b/src/todoit/linearAlgebra/leastsqTest.py
@@ -0,0 +1,45 @@
+# -*- coding: utf-8 -*-
+
+'''
+Created on 2016年5月19日
+@author: todoit
+'''
+
+import numpy as np
+from scipy.optimize import leastsq
+import pylab as pl
+
+def func(x, p):
+    """
+    数据拟合所用的函数: A*sin(2*pi*k*x + theta)
+    """
+    A, k, theta = p
+    return A*np.sin(2*np.pi*k*x+theta)   
+
+def residuals(p, y, x):
+    """
+    实验数据x, y和拟合函数之间的差，p为拟合需要找到的系数
+    """
+    return y - func(x, p)
+
+x = np.linspace(0, -2*np.pi, 100)
+A, k, theta = 10, 0.34, np.pi/6 # 真实数据的函数参数
+y0 = func(x, [A, k, theta]) # 真实数据
+y1 = y0 + 2 * np.random.randn(len(x)) # 加入噪声之后的实验数据    
+
+p0 = [7, 0.2, 0] # 第一次猜测的函数拟合参数
+
+# 调用leastsq进行数据拟合
+# residuals为计算误差的函数
+# p0为拟合参数的初始值
+# args为需要拟合的实验数据
+plsq = leastsq(residuals, p0, args=(y1, x))
+
+print(u"真实参数:", [A, k, theta] )
+print(u"拟合参数", plsq[0]) # 实验数据拟合后的参数
+
+pl.plot(x, y0, label=u"真实数据")
+pl.plot(x, y1, label=u"带噪声的实验数据")
+pl.plot(x, func(x, plsq[0]), label=u"拟合数据")
+pl.legend()
+pl.show()
\ No newline at end of file
diff --git a/src/todoit/linearAlgebra/load_MNIST.py b/src/todoit/linearAlgebra/load_MNIST.py
new file mode 100644
index 0000000..fe34e9d
--- /dev/null
+++ b/src/todoit/linearAlgebra/load_MNIST.py
@@ -0,0 +1,113 @@
+#encoding=utf-8
+
+import numpy as np
+
+
+def load_MNIST_images(filename):
+	"""loadMNISTImages returns a 28x28x[number of MNIST images] matrix containing
+	the raw MNIST images.
+	"""
+	
+	f = open(filename, 'rb')
+
+	assert f != -1, 'Could not open %s' % filename
+
+	magic = np.fromfile(f, dtype='>i4', count=1)
+	assert magic == 2051, 'Bad magic number in %s' % filename
+
+	numImages = np.fromfile(f, dtype='>i4', count=1)
+	numRows = np.fromfile(f, dtype='>i4', count=1)
+	numCols = np.fromfile(f, dtype='>i4', count=1)
+
+	images = np.fromfile(f, dtype='B')
+	images = images.reshape(numImages, numCols, numRows)
+	
+	f.close()
+
+	# Reshape to #pixels x #examples
+	images = images.reshape(images.shape[0], images.shape[1]*images.shape[2])
+	# Convert to double and rescale to [0,1]
+	images = images.astype(np.double)/255.0
+
+	return images
+    
+
+def load_MNIST_labels(filename):
+	"""loadMNISTLabels returns a [number of MNIST images]x1 matrix containing
+	the labels for the MNIST images
+	"""
+
+	f = open(filename, 'rb')
+	assert f != -1, 'Could not open %s' % filename
+
+	magic = np.fromfile(f, dtype='>i4', count=1)
+	assert magic == 2049, 'Bad magic number in %s' % filename
+	
+	numLabels = np.fromfile(f, dtype='>i4', count=1)
+	
+	labels = np.fromfile(f, dtype='B')
+	
+	assert labels.shape[0] == numLabels, 'Mismatch in label count'
+	
+	f.close()
+	
+	return labels
+
+
+def get_data(Only0=True, N=4000):
+    """
+    Only01=True: 只选取label=0或1的图像
+    Only01=False: 所有0-9的图像
+    N：训练数据长度，默认测试数据和训练数据一样长
+    """
+    images = load_MNIST_images('./data/train-images-idx3-ubyte')
+    labels = load_MNIST_labels('./data/train-labels-idx1-ubyte')
+
+    if Only0:
+        """
+        #普通实现
+        images_01=[]
+        labels_01=[]
+        for i in xrange(labels.size):
+            if labels[i]==0 or labels[i]==1:
+                labels_01.append(labels[i])
+                images_01.append(images[i,:])
+                
+        
+        images_01 = np.asarray(images_01)
+        labels_01 = np.asarray(labels_01)
+        """
+        
+        # numpy实现
+        index = np.where(labels<1)
+        images_01 = images[index[0],:]
+        labels_01 = labels[index[0]]
+        
+        assert (2*N)<images_01.shape[0], "N is too larger than data length"
+        images_s = scale_n(images_01[:N+N, :])
+        labels_s = labels_01[:N+N]         
+    else:
+        assert (2*N)<images.shape[0], "N is too larger than data length"
+        images_s = scale_n(images[:N+N, :])
+        labels_s = labels[:N+N] 
+            
+    X = np.insert(images_s, 0, 1, axis=1) 
+
+    train_X = X[:N, :] #前400行为训练数据
+    train_y = labels_s[:N]
+    train_y.shape = (train_y.shape[0],1)
+
+    test_X = X[N:, :]
+    test_y = labels_s[N:]
+    test_y.shape = (test_y.shape[0],1)
+
+    return train_X,train_y,test_X,test_y
+
+
+def scale_n(x):
+    x = np.double(x)
+    m = x.mean(axis=0)
+    s = x.std(axis=0)+0.1
+    return (x-m)/(s)
+
+    
\ No newline at end of file
diff --git a/src/todoit/linearAlgebra/pca01.py b/src/todoit/linearAlgebra/pca01.py
new file mode 100644
index 0000000..abdbc85
--- /dev/null
+++ b/src/todoit/linearAlgebra/pca01.py
@@ -0,0 +1,43 @@
+#!/usr/bin/env python
+# coding: utf-8
+#copyRight by heibanke
+
+import numpy as np
+import matplotlib.pyplot as plt  
+
+#pca主成分分析
+def pca(dataMat, topNfeat=5):  
+    #print(dataMat)
+    meanVals = np.mean(dataMat, axis=0)  
+    print(meanVals)
+    meanRemoved = dataMat - meanVals                #减去均值  
+    covMat = meanRemoved.T.dot(meanRemoved)         #求协方差方阵  
+    eigVals, eigVects = np.linalg.eig(covMat)       #求特征值和特征向量  
+    eigValInd = np.argsort(eigVals)                 #对特征值进行排序  
+    eigValInd = eigValInd[:-(topNfeat + 1):-1]    
+    redEigVects = eigVects[:, eigValInd]            #除去不需要的特征向量  
+    lowDDataMat = meanRemoved.dot(redEigVects)      #求新的数据矩阵  
+    reconMat = (lowDDataMat.dot(redEigVects.T)) + meanVals  
+    reduceData = lowDDataMat + np.mean(dataMat)
+
+    return reduceData,reconMat  
+    
+N=100
+x=np.linspace(2,4,N)
+y=x*2-4
+
+x1=x+(np.random.rand(N)-0.5)*1.5
+y1=y+(np.random.rand(N)-0.5)*1.5
+
+data = np.array([x1,y1])
+a,b=pca(data.T,1)
+
+plt.plot(x,y,color='g',linestyle='-',marker='',label='ideal') 
+plt.plot(x1,y1,color='b',linestyle='',marker='o',label='noise')
+plt.plot(b[:,0],b[:,1],color='r',linestyle='',marker='>',label='recon')
+plt.plot(a[:,0],np.zeros(N),color='k',linestyle='',marker='*',label='lowD')
+
+plt.legend()
+plt.axis('equal')
+
+plt.show()
\ No newline at end of file
diff --git a/src/todoit/linearAlgebra/solutions_3.py b/src/todoit/linearAlgebra/solutions_3.py
new file mode 100644
index 0000000..8335c91
--- /dev/null
+++ b/src/todoit/linearAlgebra/solutions_3.py
@@ -0,0 +1,69 @@
+#!/usr/bin/env python
+# coding: utf-8
+#copyRight by heibanke
+
+import numpy as np  
+import time
+
+# for hw_3-1
+"""
+两个向量a=[1,2,3],b=[1,1,1]
+如何在a,b的平面上找到一个向量和a垂直。
+"""
+# for hw_3-2
+def fourier(x,y,n):
+    m = []
+    for i in xrange(n):
+        m.append(np.cos(x*i+x))
+        m.append(np.sin(x*i+x))
+
+    mx = np.mat(m).T
+
+    y2 = y.reshape(y.shape[0],1)-np.mean(y)
+
+    w=np.linalg.inv(mx.T*mx)*mx.T*y2
+
+    yw = np.array(mx*w)+np.mean(y)
+    yw.shape = (yw.shape[0],)
+    return yw
+  
+    
+# for hw_3-3
+from matplotlib import pyplot as plt
+import matplotlib.animation as animation
+
+def eigshow(A):
+    w=np.linspace(0,2*np.pi,100)
+    x=np.array([np.cos(w),np.sin(w)])
+    ax = A.dot(x)
+    
+    def update(num):
+        s1.set_data(x[:, 0:num])
+        s2.set_data(ax[:, 0:num])
+        return s1,s2
+
+    fig1 = plt.figure()
+
+    s1, = plt.plot([], [], 'ro')
+    s2, = plt.plot([], [], 'bo')
+    plt.xlim(-4, 4)
+    plt.ylim(-4, 4)
+    plt.xlabel('x')
+    plt.title('Animation2')
+
+    line_ani = animation.FuncAnimation(fig1, update, 100,
+                                       interval=50, blit=False, repeat=False)
+                                       
+    plt.show()
+
+"""
+########################################################
+#   下节课介绍内容
+#
+#
+#
+#
+#
+#
+# for hw_3-4    
+"""
\ No newline at end of file
diff --git a/src/todoit/linearAlgebra/svd_demo.py b/src/todoit/linearAlgebra/svd_demo.py
new file mode 100644
index 0000000..32f1030
--- /dev/null
+++ b/src/todoit/linearAlgebra/svd_demo.py
@@ -0,0 +1,33 @@
+#!/usr/bin/python
+# -*- coding: utf-8 -*
+# Copy Right by heibanke
+
+import numpy as np
+from matplotlib import pyplot as plt
+
+A=np.array([[-0.2,-1],[1.1,0.5]])
+U,s,V=np.linalg.svd(A)
+S=np.array([[s[0],0],[0,s[1]]])
+
+fig = plt.figure()
+ax0 = fig.add_subplot(221)
+ax1 = fig.add_subplot(222)
+ax2 = fig.add_subplot(223)
+ax3 = fig.add_subplot(224)
+
+def plot_2D_mat(M,ax,text=""):
+    ax.plot([0,M[0,0]],[0,M[1,0]],'b-o')
+    ax.plot([0,M[0,1]],[0,M[1,1]],'r-o')
+    ax.set_title(text)
+    ax.axis('equal')
+    ax.set_xlim([-1.5,1.5])
+    ax.set_ylim([-1.5,1.5])
+    ax.grid(True)
+    
+
+plot_2D_mat(np.eye(2),ax0,"origin")
+plot_2D_mat(A,ax1,"A (USV) Matrix")
+plot_2D_mat(V.T,ax2,"V Matrix")
+plot_2D_mat(S.dot(V.T),ax3,"SV Matrix")
+
+plt.show()
\ No newline at end of file
diff --git a/src/todoit/linearAlgebra/test.py b/src/todoit/linearAlgebra/test.py
new file mode 100644
index 0000000..8ff2db2
--- /dev/null
+++ b/src/todoit/linearAlgebra/test.py
@@ -0,0 +1,8 @@
+# -*- coding: utf-8 -*-
+
+'''
+Created on 2016年6月11日
+@author: todoit
+'''
+
+import numpy as np
diff --git a/src/todoit/linearAlgebra/zuixiao2.py b/src/todoit/linearAlgebra/zuixiao2.py
new file mode 100644
index 0000000..6522fa2
--- /dev/null
+++ b/src/todoit/linearAlgebra/zuixiao2.py
@@ -0,0 +1,46 @@
+#!/usr/bin/python
+# -*- coding: utf-8 -*-
+#copyRight by heibanke 
+
+import numpy as np  
+import matplotlib.pyplot as plt  
+from scipy.optimize import leastsq
+
+x = np.linspace(0, -2*np.pi, 1000)
+    
+y = 10*np.sin(2*np.pi*0.34*x+np.pi/6)   
+
+y1 = y + 2 * np.random.randn(len(x)) # 加入噪声之后的实验数据 
+
+##################################
+### write your code to gen A,b
+m = []
+for i in range(9):
+    print(i)
+    m.append(x**(i))
+    print(m)
+m.append(0.2*np.pi*x)
+
+A = np.array(m).T
+b = y1.reshape(y1.shape[0],1)
+
+
+##################################
+
+def projection(A,b):
+    ####
+    # return A*inv(AT*A)*AT*b
+    ####
+    AA = A.T.dot(A)
+    w=np.linalg.inv(AA).dot(A.T).dot(b)
+    print(w)
+    return A.dot(w)
+
+yw = projection(A,b)
+yw.shape = (yw.shape[0],)
+
+plt.plot(x,y,color='g',linestyle='-',marker='') 
+plt.plot(x,y1,color='m',linestyle='',marker='o')
+plt.plot(x,yw,color='r',linestyle='-',marker='.')
+
+plt.show()